Malliavin Differentiability of the Heston Volatility and Applications to Option Pricing

Abstract

We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of the first author in order to derive approximate option pricing formulas in the context of the Heston model. Numerical results are given.

Keywords: Malliavin calculus, stochastic volatility models, Heston model, Cox-Ingersoll-Ross process, Hull and White formula, Option pricing

JEL Classification: C02, G13